If y varies inversely as x, and y=2/5 when x=2, find y when x=1

Inverse Variation

Inverse Variation

The statement "y varies inversely as x means that when x increases, ydecreases by the same factor. In other words, the expression xy is constant:

xy = k    

where k is the constant of variation.

We can also express the relationship between x and y as:

y =      

where k is the constant of variation.

Since k is constant, we can find k given any point by multiplying the x-coordinate by the y-coordinate. For example, if y varies inversely as x, and x = 5 when y = 2, then the constant of variation is k = xy = 5(2) = 10. Thus, the equation describing this inverse variation is xy = 10 or y = .

Example 1: If y varies inversely as x, and y = 6 when x = , write an equation describing this inverse variation.

k = (6) = 8  

xy = 8 or y =  

Example 2: If y varies inversely as x, and the constant of variation is k = , what is y when x = 10?

xy =  

10y =  

y = × = × =  

k is constant. Thus, given any two points (x1, y1) and (x2, y2) which satisfy the inverse variation, x1y1 = k and x2y2 = k. Consequently, x1y1 = x2y2 for any two points that satisfy the inverse variation.

Example 3: If y varies inversely as x, and y = 10 when x = 6, then what is y when x = 15?

x1y1 = x2y2  

6(10) = 15y  

60 = 15y  

y = 4  

Thus, when x = 6, y = 4.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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i need more details

step-by-step explanation: